Question

at the rate per cent per annum will a sum of rs.7500 amount RS.8427 in 2 year compounded annually​

Answer 1

AnswEr :

$\bf{ Given}\begin{cases}\sf{Principal = Rs. \:7500}\\\sf{Amount = Rs.\:8427}\\ \sf{Time = 2 \:years}\\\sf{Rate = ?\% \:p.a} \end{cases}$

• Amount of Compound Interest will be :

$\longrightarrow \tt{Amount = P \times \bigg(1+\dfrac{r}{100} \bigg)^{t}}\\\\\longrightarrow \tt{8427 =7500\times \bigg(1 +\dfrac{r}{100} \bigg)^{2}} \\ \\\longrightarrow \tt{ \cancel\dfrac{8427}{7500}=\bigg(1 +\dfrac{r}{100} \bigg)^{2}} \\ \\\longrightarrow \tt{\dfrac{2809}{2500}=\bigg(1 +\dfrac{r}{100} \bigg)^{2}} \\ \\\longrightarrow \tt{ \sqrt{ \dfrac{2809}{2500}}=1 +\dfrac{r}{100}} \\ \\\longrightarrow \tt{ \sqrt{ \dfrac{53 \times 53}{50 \times 50}}=1 +\dfrac{r}{100}} \\ \\\longrightarrow \tt{ \dfrac{53}{50}=1 +\dfrac{r}{100}} \\ \\\longrightarrow \tt{ \dfrac{53}{50} - 1=\dfrac{r}{100}} \\ \\\longrightarrow \tt{ \dfrac{53 - 50}{50}=\dfrac{r}{100}} \\ \\\longrightarrow \tt{ \dfrac{3}{ \cancel{50}}=\dfrac{r}{\cancel{100}}} \\ \\\longrightarrow \tt{3 = \dfrac{r}{2} } \\ \\\longrightarrow \tt3 \times 2 = r \\ \\\longrightarrow \large\boxed{ \red{\tt Rate = 6\% \:p.a.}}$

⠀

∴ Rate of Interest will be 6% per annum.

Answer 2

Present value, P = Rs.7500

Amount, A = Rs.8427

Time, n = 2 years

Now,

Amount (A) = P (1 + R/100)n

⇒ 8427 = 7500 (1 + R/100)2

⇒ (1 + R/100)2 = 8427/7500

⇒ (1 + R/100)2 = (53/50)2

⇒ (1 + R/100) = (53/50)

⇒ R/100 = 53/50 – 1

⇒ R/100 = (53 – 50)/50

⇒ R = 3/50 × 100

⇒ R = 6

∴ Rate = 6%